Quantum bit multi-state reset

ABSTRACT

Apparatus and methods for resetting a qubit. In one aspect, an apparatus includes a qubit, wherein the qubit operates over a qubit frequency spectrum with a first flux-insensitive point and a second flux-insensitive point. The apparatus further includes a readout resonator, wherein the readout resonator operates at a readout resonator frequency in-between the first flux insensitive point and the second flux-insensitive point. The apparatus further includes a frequency controller that is configured to control the frequency of the qubit such that during a reset operation the frequency of the qubit is adjusted relative to the readout resonator frequency and the qubit is reset.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation application of, and claims priorityto, U.S. patent application Ser. No. 16/465,341, now U.S. Pat. No.10,628,753, titled “QUANTUM BIT MULTI-STATE RESET,” filed on May 30,2019, which application is a U.S. National Stage application of WIPOPatent Application No. PCT/US2016/065278, entitled “QUANTUM BITMULTI-STATE RESET,” filed Dec. 7, 2016. The disclosure of the foregoingapplications incorporated herein by reference in their entirety for allpurposes.

BACKGROUND

This specification relates to quantum computing.

Resetting a quantum bit is a task in quantum computing, as well as otherapplications.

SUMMARY

This specification describes technologies relating to quantum hardwareand methods for resetting multiple qubit states using a readoutresonator.

In general, one innovative aspect of the subject matter described inthis specification can be embodied in an apparatus including a qubit,wherein the qubit operates over a qubit frequency spectrum with a firstflux-insensitive point and a second flux-insensitive point; a readoutresonator, wherein the readout resonator operates at a readout resonatorfrequency in-between the first flux insensitive point and the secondflux-insensitive point; and a frequency controller configured to controlthe frequency of the qubit such that during a reset operation thefrequency of the qubit is adjusted relative to the readout resonatorfrequency and the qubit is reset.

The foregoing and other implementations can each optionally include oneor more of the following features, alone or in combination. In someimplementations the frequency controller is further configured tocontrol the frequency of the qubit such that during a computationaloperation the qubit operates at the first flux-insensitive point or thesecond flux-insensitive point.

In some implementations the qubit comprises an asymmetricsuperconducting quantum interference device (SQUID).

In some implementations the location of the first flux-insensitive pointand the second flux-insensitive point in the qubit frequency spectrumdepend on an asymmetry factor of the SQUID.

In some implementations the ratio of the frequency of the firstflux-insensitive point to the frequency of the second flux-insensitivepoint depends on the asymmetry factor of the SQUID.

In some implementations the asymmetry factor of the SQUID is given by

${A = \frac{1 + R^{2}}{1 - R^{2}}},{R = \frac{\sqrt{A - 1}}{\sqrt{A + 1}}}$

where A represents the asymmetry factor, R represents the ratio of thefrequency of the first flux-insensitive point to the frequency of thesecond flux-insensitive point and A>1, R<1.

In some implementations, to adjust the qubit frequency relative to thereadout resonator frequency, the frequency controller is configured toset the qubit frequency at or near the resonator frequency.

In some implementations during a reset operation the frequencycontroller is configured to apply adiabatic swapping to adjust thefrequency of the qubit relative to the readout resonator frequency.

In some implementations the first flux-insensitive point is lower thanthe second flux-insensitive point, and wherein during a computationaloperation the qubit operates at the lower flux-insensitive point.

In some implementations the readout resonator frequency is at least apredetermined distance away from both the first flux-insensitive pointand the second flux-insensitive point.

In some implementations the qubit is an Xmon qubit.

In some implementations the readout resonator operates at about 6.65GHz.

In some implementations the first flux-insensitive point is at about4.5GHz and the second flux-insensitive point is at about 7.2 GHz.

Another innovative aspect of the subject matter described in thisspecification can be embodied in an apparatus including a qubit, whereinthe qubit operates at a qubit frequency over a qubit frequency spectrum;a readout resonator, wherein the readout resonator operates at a readoutresonator frequency below the qubit frequency; and a frequencycontroller configured to control the frequency of the qubit such thatduring a reset operation the frequency of the qubit is adjusted relativeto the readout resonator frequency and the qubit is reset.

The foregoing and other implementations can each optionally include oneor more of the following features, alone or in combination. In someimplementations the apparatus further comprises a Purcell filter,wherein the Purcell filter is centered around a Purcell filterfrequency.

In some implementations the Purcell filter frequency is lower than thequbit operating frequency.

In some implementations the Purcell filter frequency is about 4.5 GHz.

In some implementations the qubit frequency spectrum comprisesfrequencies between about 4.5 and 6.5 GHz.

In some implementations the readout resonator operates at about 1 GHzbelow the qubit operating frequency.

In some implementations the qubit comprises a superconducting qubit.

In some implementations, to adjust the qubit frequency relative to thereadout resonator frequency, the frequency controller is configured toset the qubit frequency at or near the resonator frequency.

In some implementations during a reset operation the frequencycontroller is configured to apply adiabatic swapping to adjust thefrequency of the qubit relative to the readout resonator frequency suchthat the qubit is reset.

The subject matter described in this specification can be implemented inparticular embodiments so as to realize one or more of the followingadvantages.

In order to implement qubit reset, the frequency at which a qubitoperates may be put on or near a frequency at which a correspondingreadout resonator operates. Unlike measurement and gate feedbackmethods, by putting the qubit frequency at or near the resonatorfrequency all qubit states may be reset simultaneously. Furthermore,putting the qubit frequency at or near the resonator frequency does notrequire any feedback mechanisms and, unlike reset methods based onquantum gates, does not propagate qubit leakage to higher states.

In systems that include superconducting qubits realized by symmetricsuperconducting quantum interference devices (SQUIDs), the highestfrequency in which the qubit operates is at a flux-insensitive point.The flux-insensitive point is a region in the frequency spectrum of thequbit that is used as a resource for dephasing. A significant source ofdephasing is flux noise. Flux noise “jitters” the qubit frequency (by anamount that is dependent on the qubit's sensitivity to flux noise),inducing dephasing. Qubit sensitivity to flux noise decreases until itreaches a minimum at the flux-insensitive point. Therefore, if theflux-insensitive point is placed above a corresponding frequency atwhich a readout resonator operates, the qubit may have to be biased farbelow the flux-insensitive point. Biasing the qubit far below theflux-insensitive point can result in the qubit becoming veryflux-sensitive and producing poor dephasing times.

Alternatively, if the frequency at which the readout resonator operatesis placed below the flux-insensitive point, additional considerationsmay have to be taken into account. For example, the thermal photonpopulation of the resonator may be higher compared to systems where thefrequency at which the readout resonator operates is not below theflux-insensitive point—incurring dephasing. Finally, allowing thereadout resonator to operate at a standard frequency and increasing thefrequency at which the qubit operates, e.g., to 7-10 GHz, results in asystem that is impractical or even infeasible to engineer.

A system implementing quantum bit multi-state reset using an asymmetricSQUID junction, as described in this specification, implements theasymmetric SQUID junction scheme to include a second flux-insensitivepoint below the frequency at which the readout resonator operates. Thesystem is able to achieve fast reset of qubit states, an increase in theassociated data rate, e.g., over one hundred fold, little to nodegradation in dephasing and is forward compatible to data qubit reset,e.g., using adiabatic swap. For example, other systems that do notperform quantum bit multi-state reset perform a control sequence thatinvolves an algorithm or computation and state reset. The algorithm cantypically take a few microseconds, and resetting the qubit statereliably without active reset requires waiting significantly longer thanthe coherence time, e.g., five times the coherence time. A systemimplementing quantum bit multi-state reset avoids these problems.

A system implementing quantum bit multi-state reset using a low readoutresonator frequency, as described in this specification, implements ascheme in which the frequency at which the readout resonator operates islower than the qubit operating frequency. Typically, operating a qubitat a frequency that is higher than a frequency at which the readoutresonator operates can cause the qubit to couple to higher modes of thereadout resonator. This in turn can cause increased T1 energyrelaxation. A system implementing quantum bit multi-state reset using alow readout resonator frequency, as described in this specification,enables the qubit to be operated at a frequency above the readoutresonator frequency with similar protection from the environment as thatwhen operating the qubit at a frequency below the readout resonatorfrequency.

Systems implementing quantum bit multi-state reset, as described in thisspecification, may be used to perform fault tolerant error correction inquantum computations to prevent correlated errors, thus improving theaccuracy and reliability of said quantum computations and systemsperforming said quantum computations.

Systems implementing quantum bit multi-state reset, as described in thisspecification, enable qubits involved in a computation to be reliablyrecycled during the computation. For example, in systems that do notimplement quantum bit multi-state reset as described in thisspecification, an ancilla qubit is typically discarded. However, in thesystems described in this specification, an ancilla qubit can beinitialized and used again in the computation. Furthermore, unlike othersystems, qubit recycling is not dependent on measurement fidelity andfeedback time.

The details of one or more implementations of the subject matter of thisspecification are set forth in the accompanying drawings and thedescription below. Other features, aspects, and advantages of thesubject matter will become apparent from the description, the drawings,and the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A depicts an example system for performing quantum bit multi-statereset using an asymmetric squid.

FIG. 1B depicts an example system for performing quantum bit multi-statereset using a low frequency readout resonator.

FIG. 1C depicts an example circuit diagram for performing quantum bitmulti-state reset.

FIG. 1D depicts an example circuit diagram for performing quantum bitmulti-state reset using a low frequency readout resonator.

FIG. 2 is an illustration of frequency versus flux for symmetric andasymmetric SQUIDs.

FIG. 3 is an illustration of the flux sensitivity of symmetric andasymmetric SQUIDs.

FIG. 4A is an illustration showing the coupling of a qubit to anenvironment including a low frequency resonator via S-parameters.

FIG. 4B is an illustration showing the quality rate of a qubit coupledto an environment including a low frequency resonator.

FIG. 5 is a flowchart of an example process for performing qubitmulti-state reset using an asymmetric junction scheme.

FIG. 6 is a flowchart of an example process for performing qubitmulti-state reset using a low frequency readout resonator scheme.

Like reference numbers and designations in the various drawings indicatelike elements.

DETAILED DESCRIPTION

This specification describes an architecture and method for resettingmultiple states of a qubit. In some cases the architecture includes aqubit realized by an asymmetric superconducting quantum interferencedevice (SQUID) that provides two flux-insensitive points of the qubitfrequency spectrum and a readout resonator that operates at a frequencyin-between the two flux-insensitive points. In other cases thearchitecture includes a qubit realized by a SQUID and a readoutresonator that operates at a frequency that is lower than the qubitoperating frequency. In both cases qubit reset is achieved by puttingthe qubit at or near resonance with the readout resonator.

Example Operating Environment

FIG. 1A depicts an example system 100 for performing qubit multi-statereset. The system 100 includes a qubit 102, a readout resonator 104 anda frequency controller 106. The readout resonator 104 and frequencycontroller 106 interact with the qubit 102. For convenience one qubit102 and one readout resonator are shown in FIG. 1A, however in someimplementations the system 100 may include multiple qubits and multiplereadout resonators.

In some implementations the qubit 102 may be a superconducting qubit,e.g., an Xmon qubit. For example, the qubit 102 may be realized by asuperconducting quantum interference device (SQUID). The qubit 102includes a set of qubit levels, e.g., two computational qubit levels 0-,1- and one or more non-computational levels that are each higher thanthe computational qubit levels. Transitions between the qubit levels,e.g., transitions from level 0- to 1-, 1- to 2-, 2- to 3-, etc., may beassociated with respective transition frequencies. The computationalqubit levels 0- and 1- are qubit levels used to perform computationaloperations, as described below. Operating a qubit at a particularfrequency may therefore describe facilitating a transition between thecomputational qubit levels using the particular frequency, e.g., using amicrowave pulse to induce a transition from 0- to 1- or from 1- to 0-.The range of frequencies that may be used to operate a qubit may be saidto form a frequency spectrum.

The qubit 102 may be frequency tunable, i.e., the frequency inducing atransition between computational qubit levels may be controllable. Asdescribed above, in some implementations the qubit 102 may be asuperconducting qubit and realized by a SQUID. In these implementationsthe frequency of the qubit 102 may be tunable via tuning a current thatflows through the SQUID, e.g., by applying an external magnetic flux tothe SQUID. In some implementations the dependency of the qubit frequencyon a tunable current may be given by a square-root of cosine.

The frequency spectrum of a qubit may include one or moreflux-insensitive points. A flux-insensitive point is a point or regionin the frequency spectrum where a qubit may operate at or over withoutbeing sensitive to changes in the current used to tune the frequency ofthe qubit, e.g., to first order. The frequency spectrum 108 of qubit 102includes multiple flux-insensitive points, e.g., flux-insensitive point110 a and flux-insensitive point 110 b. In some implementations thefirst flux-insensitive point 110 a may correspond to a frequency ofabout 4.5 GHz. In some implementations the second flux-insensitive point110may correspond to a frequency of about 7.2 GHz. Exampleflux-insensitive points are illustrated below with reference to FIG. 2.

As described above, in some implementations the qubit 102 may berealized by a SQUID. In these implementations the SQUID may be anasymmetric SQUID. An asymmetric SQUID includes two Josephson junctionsin parallel in a superconducting loop. A current I enters the SQUID andsplits into two paths with respective junction critical currents I₁ andI₂. An asymmetric SQUID is a SQUID whose respective junction criticalcurrents I₁ and I₂ are not equal, namely I₁ ≠I₂.

The location of the flux-insensitive points of the qubit frequencyspectrum 108, e.g., flux-insensitive point 110 a and flux-insensitivepoint 110 b, may depend on an asymmetry factor of the asymmetric SQUID.For example, given a SQUID with junction critical currents I₁ and I₂, acorresponding critical current I_(c) ^(SQUID) may be derived as afunction of applied magnetic flux Φ. As a first step, I_(c) ^(SQUID)maybe determined using the below equations:

$\mspace{76mu} {{\varphi_{12}(a)} = {\varphi_{a} - {\frac{2e}{\hslash}{\int_{{path}\mspace{14mu} a}{\overset{\rightarrow}{A} \cdot \overset{\rightarrow}{ds}}}}}}$$\mspace{76mu} {{\varphi_{12}(b)} = {\varphi_{b} - {\frac{2e}{\hslash}{\int_{{path}\mspace{14mu} b}{\overset{\rightarrow}{A} \cdot \overset{\rightarrow}{ds}}}}}}$     φ₁₂(a) = φ₁₂(b)${\varphi_{a} - \varphi_{b}} = {{{- \frac{2e}{\hslash}}{\oint_{SQUID}{\overset{\rightarrow}{A} \cdot \overset{\rightarrow}{ds}}}} = {{{- \frac{2e}{\hslash}}{\int_{surface}{\overset{\rightarrow}{B} \cdot \overset{\rightarrow}{dA}}}} = {{{- \frac{2e}{\hslash}}\Phi} = {- {\frac{2{\pi\Phi}}{~\Phi_{0}}.}}}}}$

Defining

$\varphi_{avg} = \frac{\varphi_{a} + \varphi_{b}}{2}$

gives

${\varphi_{a} = {\varphi_{avg} - {\frac{e}{\hslash}\Phi}}},{\varphi_{b} = {\varphi_{avg} - {\frac{e}{\hslash}\Phi}}}$and$I_{C}^{SQUID} = {{I_{1}{\sin \left( {\varphi_{avg} - \frac{\pi\Phi}{\Phi_{0}}} \right)}} + {I_{2}{{\sin \left( {\varphi_{avg} + \frac{\pi\Phi}{\Phi_{0}}} \right)}.}}}$

For an asymmetric SQUID, the above may be solved for two regions ofinterest, namely the flux-insensitive points, e.g., flux insensitivepoints 110 a and 110 b. The points may lie at Φ/Φ₀=0, ½.

When Φ/Φ₀=0, the critical current I_(C) ^(SQUID) may be given by

I _(C) ^(SQUID) =I ₁ +I ₂.

When Φ/Φ₀=½, the critical current I_(C) ^(SQUID) may be given by

I _(C) ^(SQUID) =I ₁ cos(ϕ_(avg))+I ₂ cos(ϕ_(avg)) I _(c) ^(SQUID) =|I ₁−I ₂|.

In some implementations, a ratio R of the frequency of the firstflux-insensitive point, e.g., flux-insensitive point 110 a, to thefrequency of the second flux-insensitive point, e.g., flux insensitivepoint 110 b, may be engineered to depend on the asymmetry factor of theSQUID, as given below in equation (1).

$\begin{matrix}{R = {\frac{f_{\min}}{f_{\max}} = \frac{\sqrt{{I_{1} - I_{2}}}}{\sqrt{I_{1} + I_{2}}}}} & (1)\end{matrix}$

In equation (1), f_(min) represents the frequency of the firstflux-insensitive point and f_(max) represents the frequency of thesecond flux-insensitive point and it is assumed that the frequency atwhich the qubit operates is proportional to the square root of thecritical current.

In some implementations the asymmetry factor A of the SQUID may be givenby equation (2) below.

$\begin{matrix}{{A = \frac{1 + R^{2}}{1 - R^{2}}},{R = \frac{\sqrt{A - 1}}{\sqrt{A + 1}}}} & (2)\end{matrix}$

In equation (2), A represents the asymmetry factor, R represents theratio of the frequency of the first flux-insensitive point to thefrequency of the second flux-insensitive point and it is assumed thatA>1, R<1, and I₁>I₂.

As described above, in some implementations the qubit 102 may beengineered such that the first flux-insensitive point 110 a is locatedat a 4.5 GHz and the second flux-insensitive point 110 b is located at7.2 GHz. Using equation (1), the ratio R of the frequency of the firstflux-insensitive point to the frequency of the second flux-insensitivepoint equals R=0.625. Using equation (2), the asymmetry factor A of theSQUID equals A=2.28. Example flux-insensitive points for a SQUID withasymmetry factor A=2.28 are shown below with reference to FIG. 2.

The qubit 102 may be used to perform computational operations, e.g.,algorithmic operations or quantum computations. During a computationaloperation, the qubit 102 operates at a frequency corresponding to aflux-insensitive point. For example, in some implementations the qubit102 may operate at the flux-insensitive point corresponding to thelowest frequency, e.g., flux-insensitive point 110 a.

The qubit 102 may undergo a reset operation, e.g., an operation thatrestores the qubit 102 to its ground state. During a reset operation,the qubit 102 operates at a frequency corresponding to the frequency atwhich the readout resonator operates. In some implementations operatingthe qubit 102 at a frequency at which the readout resonator operatesincludes sweeping the frequency at which the qubit operates past thefrequency at which the readout resonator operates to perform downwardqubit level transitions, i.e., performing multi-state qubit reset.Performing a qubit reset operation is described in more detail belowwith reference to FIG. 5.

The readout resonator 104 operates at a readout resonator frequency. Insome implementations the readout resonator frequency is a frequency thatlies between the frequencies corresponding to the flux-insensitivepoints 110 a and 110 b. For example, as described above, in someimplementations the first flux-insensitive point 110 a may correspond toa frequency of about 4.5 GHz and the second flux-insensitive point 110 bmay correspond to a frequency of about 7.2 GHz. In this example, thereadout resonator may operate at a readout resonator frequency of about6.65GHz. In some implementations the readout resonator frequency may beat least a predetermined distance away from both the firstflux-insensitive point 110 a and the second flux-insensitive point 110 bso that unwanted qubit reset does not occur during a computationaloperation.

The frequency controller 106 is configured to control the frequency ofthe qubit 102. The frequency controller 106 controls the frequency ofthe qubit 102 such that during a reset operation the frequency of thequbit may be adjusted relative to the readout resonator frequency inorder to facilitate qubit reset. For example, the frequency controller106 may be configured to put the frequency at which the qubit 102operates at or near the resonator frequency. In some implementations thefrequency controller may apply adiabatic swapping to adjust thefrequency at which the qubit 102 operates relative to the frequency atwhich the readout resonator 104 operates in order to facilitate qubitreset. Performing qubit multi-state reset using a frequency controlleris described in more detail below with reference to FIGS. 4 and 5.

FIG. 1B depicts an example system 110 for performing quantum bitmulti-state reset using a low frequency readout resonator. The system110 includes a qubit 112, a readout resonator 114 and a frequencycontroller 116. The readout resonator 114 and the frequency controller116 interact with the qubit 112. For example, the readout resonator 114and qubit 112 may interact through a capacitive coupling. Forconvenience one qubit 112 and one readout resonator 114 are shown inFIG. 1B, however in some implementations the system 110 may includemultiple qubits and multiple readout resonators.

In some implementations the qubit 112 may be a superconducting qubit,e.g., an Xmon qubit. For example, the qubit 112 may be realized by asuperconducting quantum interference device (SQUID). The qubit 112includes a set of qubit levels, e.g., two computational qubit levels 0-,1- and one or more non-computational levels that are each higher thanthe computational qubit levels. Transitions between the qubit levels,e.g., transitions from level 0- to 1-, 1- to 2-, 2- to 3-, etc., may beassociated with respective transition frequencies.

The computational qubit levels 0- and 1- are qubit levels used toperform computational operations, e.g., algorithmic operations orquantum computations. Operating a qubit at a particular frequency maydescribe facilitating a transition between the computational qubitlevels using the particular frequency, e.g., using a microwave pulse toinduce a transition from 0- to 1- or from 1- to 0-. The range offrequencies that may be used to operate a qubit may be said to form afrequency spectrum. In some implementations the qubit frequency spectrumincludes frequencies between about 4.5 GHz and 6.5 GHz.

The qubit 112 may also undergo a reset operation, e.g., an operationthat restores the qubit 112 to its ground state. During a resetoperation, the qubit 112 operates at a frequency corresponding to thefrequency at which the readout resonator operates. In someimplementations operating the qubit 112 at a frequency at which thereadout resonator operates includes sweeping the frequency at which thequbit operates past the frequency at which the readout resonatoroperates to perform downward qubit level transitions, i.e., performingmulti-state qubit reset. Performing a qubit reset operation is describedin more detail below with reference to FIG. 6.

The qubit 112 may be frequency tunable, i.e., the frequency inducing atransition between computational qubit levels may be controllable. Asdescribed above, in some implementations the qubit 112 may be asuperconducting qubit and realized by a SQUID. In these implementationsthe frequency of the qubit 112 may be tunable via tuning a current thatflows through the SQUID, e.g., by applying an external magnetic flux tothe SQUID. In some implementations the dependency of the qubit frequencyon a tunable current may be given by a square-root of cosine.

The readout resonator 114 operates at a readout resonator frequency. Insome implementations the readout resonator frequency is a frequency thatis below the qubit operating frequency. For example, the readoutresonator may operate at a readout resonator frequency that is about 1GHz below the qubit operating frequency. In some implementations thereadout resonator may operate at 4.5 GHz.

Optionally, the system 110 may include a Purcell filter. The Purcellfilter may be coupled to the readout resonator 114, e.g., through aninductive coupling realized via a voltage tap. The Purcell filter may becentered around a Purcell filter frequency. In some implementations thePurcell filter frequency may also be below the qubit operatingfrequency.

The frequency controller 116 is configured to control the frequency ofthe qubit 112. The frequency controller 116 controls the frequency ofthe qubit 112 such that during a reset operation the frequency of thequbit may be adjusted relative to the readout resonator frequency inorder to facilitate qubit reset. For example, the frequency controller116 may be configured to put the frequency at which the qubit 112operates at or near the resonator frequency. In some implementations thefrequency controller may apply adiabatic swapping to adjust thefrequency at which the qubit 112 operates relative to the frequency atwhich the readout resonator 114 operates in order to facilitate qubitreset. Performing qubit multi-state reset using a frequency controlleris described in more detail below with reference to FIG. 6. Thefrequency controller 116 may also be configured to control the frequencyof the qubit 112 such that during a computational operation the qubitoperates at a qubit operating frequency in the frequency spectrum.

FIG. 1C depicts a diagram 120 of an example circuit for performing qubitmulti-state reset. For example, the example circuit diagram 120 mayrealize the example systems 100 and 110 described above with referenceto FIGS. 1A and 1B, respectively.

The diagram 120 includes a qubit 122, e.g., a transmon qubit. The qubit122 may be capacitively coupled to a resonator 124. The resonator 124may be inductively coupled to a bandpass Purcell filter 128, e.g., withQ 30. The resonator 124 may be driven by an arbitrary waveform generator(AWG) 130 connected to the filter 128. Dispersed photons may be measuredby a low noise, impedance matched parametric amplifier (IMPA) 126 thatmay also be connected to the filter 128.

FIG. 1D depicts a diagram 150 of an example circuit for performing qubitmulti-state reset using a low frequency readout resonator. For example,the example circuit diagram 150 may realize the example system 110described above with reference to FIG. 1B.

The example circuit diagram 150 includes a qubit 152. The qubit 152 maybe coupled to a resonator 154, e.g., through capacitive coupling. Theresonator 154 may be coupled to a Purcell filter 156, e.g., throughinductive coupling. In some implementations the Purcell filter may be alambda/2 Purcell filter. For illustrative purposes only, the diagram 150includes example values of circuit parameters. In some implementations,values of circuit parameters that are different to those shown in FIG.1D may be used.

FIG. 2 is an illustration 200 of frequency versus flux for qubitsrealized by superconducting quantum interference devices (SQUIDs), asdescribed above with reference to FIG. 1A. The x-axis of illustration200 represents magnetic flux Φ/Φ₀ applied to a qubit. The y-axis ofillustration 200 represents normalized frequency at which the qubitoperates. The illustration 200 shows two different example plots, i.e.,plots 202 and 204, of qubit frequency versus magnetic flux.

Example plot 202 illustrates qubit frequency versus magnetic flux for asymmetric SQUID, e.g., a SQUID whose asymmetry factor A=1.0. The plot202 shows that a qubit realized by a symmetric SQUID includes oneflux-insensitive point or region, e.g., point 206 corresponding to zeromagnetic flux.

Example plot 204 illustrates qubit frequency versus magnetic flux for anasymmetric SQUID, e.g., a SQUID whose asymmetry factor A=2.28. The plot204 shows that a qubit realized by an asymmetric SQUID includes twoflux-insensitive points or regions, e.g., point 206 corresponding tozero magnetic flux and point 208 corresponding to magnetic flux equal to0.5.

FIG. 3 is an illustration 300 of flux sensitivity for qubits realized bysuperconducting quantum interference devices (SQUIDs), as describedabove with reference to FIG. 1A. The x-axis of illustration 300represents frequency in GHz at which the qubit operates. The y-axis ofillustration 300 represents flux sensitivity of the qubit. Theillustration 300 shows two different example plots, i.e., plots 302 and304, of qubit flux sensitivity.

Example plot 302 illustrates flux sensitivity for qubits realized by asymmetric SQUID, e.g., a SQUID whose asymmetry factor A=1.0. The plot302 shows that the frequency region 5.8-5.3 GHz provides fluxsensitivity <6.0.

Example plot 304 illustrates flux-insensitivity for qubits realized byan asymmetric SQUID, e.g., a SQUID whose asymmetry factor A=2.28.

FIG. 4A is an example illustration 400 showing the coupling of a qubitto an environment including a low frequency resonator via S-parameters(scattering parameters). For example, the qubit may be coupled to anenvironment including a readout resonator and Purcell filter, asdescribed above with reference to FIGS. 1B and 1D.

The example illustration 400 includes an x-axis representing qubitfrequency in GHz, and a y-axis representing decibels. The illustrationplots a transition from a third qubit level to a first qubit level 402.The illustration further plots a transition from a third qubit level toa second qubit level 404. The illustration further plots a transitionfrom a second qubit level to a first qubit level 406. Each of the plots402, 404 and 406 show a low signal strength when the qubit frequency isbetween 4 GHz and 6 GHz, i.e., at a qubit operating frequency. Theillustration shows that the qubit is well protected from theenvironment, e.g., that the qubit does not couple to higher modes of thereadout resonator.

FIG. 4B is an example illustration 450 showing the quality value of aqubit coupled to an environment including a low frequency resonator. Forexample, the qubit may be coupled to an environment including a readoutresonator and Purcell filter, as described above with reference to FIGS.1B and 1D.

The example illustration 450 includes an x-axis representing qubitfrequency, and a y-axis representing a quality value (Q-value) for thequbit. The example illustration 450 shows that the Q-value reaches atarget value of 10{circumflex over ( )}7 faster on the higher qubitfrequency side than the lower qubit frequency side—thus illustratingthat the low frequency resonator system, e.g., that described above withreference to FIGS. 1B and 1D, functions comparably, if not better, thana high frequency resonator system, i.e., a system including a readoutresonator whose operating frequency is higher than the qubit operatingfrequency.

Programming the Hardware

FIG. 5 is a flowchart of an example process for performing qubitmulti-state reset using an asymmetric junction scheme. For example, theprocess 500 may be performed by the frequency controller 106 of system100 described above with reference to FIG. 1A. For convenience, theprocess 500 is described as resetting a single qubit. However, theprocess 500 may be performed in parallel for systems that includemultiple qubits.

The system accesses a quantum system (step 502). The quantum system mayinclude a qubit and a readout resonator, e.g., qubit 102 and readoutresonator 104 described above with reference to FIG. 1A. The qubitoperates over a qubit frequency spectrum with a first flux-insensitivepoint and a second flux-insensitive point. The readout resonatoroperates at a readout resonator frequency in-between the first fluxinsensitive point and the second flux-insensitive point. In someimplementations the readout resonator frequency may be at least apredetermined distance away from both the first flux-insensitive pointand the second flux-insensitive point.

As described above with reference to FIG. 1A, in some implementationsthe qubit may be realized by an asymmetric superconducting quantuminterference device (SQUID). The location of the first flux-insensitivepoint and the second flux-insensitive point in the qubit frequencyspectrum may depend on an asymmetry factor of the SQUID. For example, insome implementations the ratio of the frequency of the firstflux-insensitive point to the frequency of the second flux-insensitivepoint depends on the asymmetry factor of the SQUID. The asymmetry factorof the SQUID may be given by equation (3) below.

$\begin{matrix}{{A = \frac{1 + R^{2}}{1 - R^{2}}},{R = \frac{\sqrt{A - 1}}{\sqrt{A + 1}}}} & (3)\end{matrix}$

In equation (3), A represents the asymmetry factor, R represents theratio of the frequency of the first flux-insensitive point to thefrequency of the second flux-insensitive point and A>1, R<1.

The system controls the frequency of the qubit such that during a resetoperation the frequency of the qubit is adjusted relative to the readoutresonator and the qubit is reset (step 504). In some implementations thesystem may adjust the qubit frequency relative to the readout resonatorfrequency by putting the qubit frequency at or near the resonatorfrequency. For example, the system may apply adiabatic swapping toadjust the frequency of the qubit relative to the readout resonatorfrequency such that the qubit is reset.

As described above with reference to FIG. 1A, the qubit may be active inor provided for use in a quantum computation. In such settings steps 502and 504 may be repeatedly performed during the quantum computation,e.g., immediately after a measurement operation associated with acomputation operation in the quantum computation.

FIG. 6 is a flowchart of an example process for performing qubitmulti-state reset using an asymmetric junction scheme. For example, theprocess 600 may be performed by the frequency controller 116 of system110 described above with reference to FIG. 1B. For convenience, theprocess 600 is described as resetting a single qubit. However, theprocess 600 may be performed in parallel for systems that includemultiple qubits.

The system accesses a quantum system (step 602). The quantum system mayinclude a qubit and a readout resonator, e.g., qubit 112 and readoutresonator 114 described above with reference to FIG. 1B. The qubitoperates at a qubit operating frequency over a frequency spectrum. Asdescribed above with reference to FIG. 1B, in some implementations thequbit may be a superconducting qubit, e.g., as realized by asuperconducting quantum interference device (SQUID). The readoutresonator operates at a readout resonator frequency below the qubitoperating frequency. In some implementations the quantum system furtherincludes a Purcell filter centered around a Purcell filter frequencythat is also below the qubit operating frequency.

The system controls the frequency of the qubit such that during a resetoperation the frequency of the qubit is adjusted relative to the readoutresonator frequency such that the qubit is reset (step 604). In someimplementations the system may adjust the qubit frequency relative tothe readout resonator frequency by putting the qubit frequency at ornear the resonator frequency. For example, the system may applyadiabatic swapping to adjust the frequency of the qubit relative to thereadout resonator frequency such that the qubit is reset.

As described above with reference to FIG. 1A, the qubit may be active inor provided for use in a quantum computation. In such settings steps 602and 604 may be repeatedly performed during the quantum computation,e.g., immediately after a measurement operation associated with acomputation operation in the quantum computation.

Embodiments of the digital and/or quantum subject matter and the digitalfunctional operations and quantum operations described in thisspecification can be implemented in digital electronic circuitry,suitable quantum circuitry or, more generally, quantum computationalsystems, in tangibly-embodied digital and/or quantum computer softwareor firmware, in digital and/or quantum computer hardware, including thestructures disclosed in this specification and their structuralequivalents, or in combinations of one or more of them. The term“quantum computational systems” may include, but is not limited to,quantum computers, quantum information processing systems, quantumcryptography systems, or quantum simulators.

Embodiments of the digital and/or quantum subject matter described inthis specification can be implemented as one or more digital and/orquantum computer programs, i.e., one or more modules of digital and/orquantum computer program instructions encoded on a tangiblenon-transitory storage medium for execution by, or to control theoperation of, data processing apparatus. The digital and/or quantumcomputer storage medium can be a machine-readable storage device, amachine-readable storage substrate, a random or serial access memorydevice, one or more qubits, or a combination of one or more of them.Alternatively or in addition, the program instructions can be encoded onan artificially-generated propagated signal that is capable of encodingdigital and/or quantum information, e.g., a machine-generatedelectrical, optical, or electromagnetic signal, that is generated toencode digital and/or quantum information for transmission to suitablereceiver apparatus for execution by a data processing apparatus.

The terms quantum information and quantum data refer to information ordata that is carried by, held or stored in quantum systems, where thesmallest non-trivial system is a qubit, i.e., a system that defines theunit of quantum information. It is understood that the term “qubit”encompasses all quantum systems that may be suitably approximated as atwo-level system in the corresponding context. Such quantum systems mayinclude multi-level systems, e.g., with two or more levels. By way ofexample, such systems can include atoms, electrons, photons, ions orsuperconducting qubits. In many implementations the computational basisstates are identified with the ground and first excited states, howeverit is understood that other setups where the computational states areidentified with higher level excited states are possible.

The term “data processing apparatus” refers to digital and/or quantumdata processing hardware and encompasses all kinds of apparatus,devices, and machines for processing digital and/or quantum data,including by way of example a programmable digital processor, aprogrammable quantum processor, a digital computer, a quantum computer,or multiple digital and quantum processors or computers, andcombinations thereof. The apparatus can also be, or further include,special purpose logic circuitry, e.g., an FPGA (field programmable gatearray), or an ASIC (application-specific integrated circuit), or aquantum simulator, i.e., a quantum data processing apparatus that isdesigned to simulate or produce information about a specific quantumsystem. In particular, a quantum simulator is a special purpose quantumcomputer that does not have the capability to perform universal quantumcomputation. The apparatus can optionally include, in addition tohardware, code that creates an execution environment for digital and/orquantum computer programs, e.g., code that constitutes processorfirmware, a protocol stack, a database management system, an operatingsystem, or a combination of one or more of them.

A digital computer program, which may also be referred to or describedas a program, software, a software application, a module, a softwaremodule, a script, or code, can be written in any form of programminglanguage, including compiled or interpreted languages, or declarative orprocedural languages, and it can be deployed in any form, including as astand-alone program or as a module, component, subroutine, or other unitsuitable for use in a digital computing environment. A quantum computerprogram, which may also be referred to or described as a program,software, a software application, a module, a software module, a script,or code, can be written in any form of programming language, includingcompiled or interpreted languages, or declarative or procedurallanguages, and translated into a suitable quantum programming language,or can be written in a quantum programming language, e.g., QCL orQuipper.

A digital and/or quantum computer program may, but need not, correspondto a file in a file system. A program can be stored in a portion of afile that holds other programs or data, e.g., one or more scripts storedin a markup language document, in a single file dedicated to the programin question, or in multiple coordinated files, e.g., files that storeone or more modules, sub-programs, or portions of code. A digital and/orquantum computer program can be deployed to be executed on one digitalor one quantum computer or on multiple digital and/or quantum computersthat are located at one site or distributed across multiple sites andinterconnected by a digital and/or quantum data communication network. Aquantum data communication network is understood to be a network thatmay transmit quantum data using quantum systems, e.g. qubits. Generally,a digital data communication network cannot transmit quantum data,however a quantum data communication network may transmit both quantumdata and digital data.

The processes and logic flows described in this specification can beperformed by one or more programmable digital and/or quantum computers,operating with one or more digital and/or quantum processors, asappropriate, executing one or more digital and/or quantum computerprograms to perform functions by operating on input digital and quantumdata and generating output. The processes and logic flows can also beperformed by, and apparatus can also be implemented as, special purposelogic circuitry, e.g., an FPGA or an ASIC, or a quantum simulator, or bya combination of special purpose logic circuitry or quantum simulatorsand one or more programmed digital and/or quantum computers.

For a system of one or more digital and/or quantum computers to be“configured to” perform particular operations or actions means that thesystem has installed on it software, firmware, hardware, or acombination of them that in operation cause the system to perform theoperations or actions. For one or more digital and/or quantum computerprograms to be configured to perform particular operations or actionsmeans that the one or more programs include instructions that, whenexecuted by digital and/or quantum data processing apparatus, cause theapparatus to perform the operations or actions. A quantum computer mayreceive instructions from a digital computer that, when executed by thequantum computing apparatus, cause the apparatus to perform theoperations or actions.

Digital and/or quantum computers suitable for the execution of a digitaland/or quantum computer program can be based on general or specialpurpose digital and/or quantum microprocessors or both, or any otherkind of central digital and/or quantum processing unit. Generally, acentral digital and/or quantum processing unit will receive instructionsand digital and/or quantum data from a read-only memory, or a randomaccess memory, or quantum systems suitable for transmitting quantumdata, e.g. photons, or combinations thereof both.

The essential elements of a digital and/or quantum computer are acentral processing unit for performing or executing instructions and oneor more memory devices for storing instructions and digital and/orquantum data. The central processing unit and the memory can besupplemented by, or incorporated in, special purpose logic circuitry orquantum simulators. Generally, a digital and/or quantum computer willalso include, or be operatively coupled to receive digital and/orquantum data from or transfer digital and/or quantum data to, or both,one or more mass storage devices for storing digital and/or quantumdata, e.g., magnetic, magneto-optical disks, or optical disks, orquantum systems suitable for storing quantum information. However, adigital and/or quantum computer need not have such devices.

Digital and/or quantum computer-readable media suitable for storingdigital and/or quantum computer program instructions and digital and/orquantum data include all forms of non-volatile digital and/or quantummemory, media and memory devices, including by way of examplesemiconductor memory devices, e.g., EPROM, EEPROM, and flash memorydevices; magnetic disks, e.g., internal hard disks or removable disks;magneto-optical disks; and CD-ROM and DVD-ROM disks; and quantumsystems, e.g., trapped atoms or electrons. It is understood that quantummemories are devices that can store quantum data for a long time withhigh fidelity and efficiency, e.g., light-matter interfaces where lightis used for transmission and matter for storing and preserving thequantum features of quantum data such as superposition or quantumcoherence.

Control of the various systems described in this specification, orportions of them, can be implemented in a digital and/or quantumcomputer program product that includes instructions that are stored onone or more non-transitory machine-readable storage media, and that areexecutable on one or more digital and/or quantum processing devices. Thesystems described in this specification, or portions of them, can eachbe implemented as an apparatus, method, or electronic system that mayinclude one or more digital and/or quantum processing devices and memoryto store executable instructions to perform the operations described inthis specification.

While this specification contains many specific implementation details,these should not be construed as limitations on the scope of what may beclaimed, but rather as descriptions of features that may be specific toparticular embodiments. Certain features that are described in thisspecification in the context of separate embodiments can also beimplemented in combination in a single embodiment. Conversely, variousfeatures that are described in the context of a single embodiment canalso be implemented in multiple embodiments separately or in anysuitable sub-combination. Moreover, although features may be describedabove as acting in certain combinations and even initially claimed assuch, one or more features from a claimed combination can in some casesbe excised from the combination, and the claimed combination may bedirected to a sub-combination or variation of a sub-combination.

Similarly, while operations are depicted in the drawings in a particularorder, this should not be understood as requiring that such operationsbe performed in the particular order shown or in sequential order, orthat all illustrated operations be performed, to achieve desirableresults. In certain circumstances, multitasking and parallel processingmay be advantageous. Moreover, the separation of various system modulesand components in the embodiments described above should not beunderstood as requiring such separation in all embodiments, and itshould be understood that the described program components and systemscan generally be integrated together in a single software product orpackaged into multiple software products.

Particular embodiments of the subject matter have been described. Otherembodiments are within the scope of the following claims. For example,the actions recited in the claims can be performed in a different orderand still achieve desirable results. As one example, the processesdepicted in the accompanying figures do not necessarily require theparticular order shown, or sequential order, to achieve desirableresults. In some cases, multitasking and parallel processing may beadvantageous.

What is claimed is:
 1. An apparatus, comprising: a qubit, wherein thequbit operates over a qubit frequency spectrum with a firstflux-insensitive point and a second flux-insensitive point; a readoutresonator, wherein the readout resonator operates at a readout resonatorfrequency in-between the first flux insensitive point and the secondflux-insensitive point; a frequency controller configured to control thefrequency of the qubit such that during a quantum computation thefrequency of the qubit is adjusted relative to the readout resonatorfrequency.
 2. The apparatus of claim 1, wherein during the quantumcomputation the frequency of the qubit is adjusted relative to thereadout resonator frequency to perform a downward qubit leveltransition.
 3. The apparatus of claim 1, wherein the frequencycontroller is further configured to control the frequency of the qubitsuch that during the quantum computation the qubit operates at the firstflux-insensitive point or the second flux-insensitive point.
 4. Theapparatus of claim 1, wherein the qubit comprises an asymmetricsuperconducting quantum interference device (SQUID), and wherein thelocation of the first flux-insensitive point and the secondflux-insensitive point in the qubit frequency spectrum depend on anasymmetry factor of the SQUID.
 5. The apparatus of claim 4, wherein theratio of the frequency of the first flux-insensitive point to thefrequency of the second flux-insensitive point depends on the asymmetryfactor of the SQUID.
 6. The apparatus of claim 5, wherein the asymmetryfactor of the SQUID is given by${A = \frac{1 + R^{2}}{1 - R^{2}}},{R = \frac{\sqrt{A - 1}}{\sqrt{A + 1}}}$where A represents the asymmetry factor, R represents the ratio of thefrequency of the first flux-insensitive point to the frequency of thesecond flux-insensitive point and A>1, R<1.
 7. The apparatus of claim 1,wherein to adjust the qubit frequency relative to the readout resonatorfrequency the frequency controller is configured to set the qubitfrequency at or near the resonator frequency.
 8. The apparatus of claim1, wherein during the quantum computation the frequency controller isconfigured to apply adiabatic swapping to adjust the frequency of thequbit relative to the readout resonator frequency.
 9. The apparatus ofclaim 1, wherein the first flux-insensitive point is lower than thesecond flux-insensitive point, and wherein during the quantumcomputation the qubit operates at the lower flux-insensitive point. 10.The apparatus of claim 1, wherein the readout resonator frequency is atleast a predetermined distance away from both the first flux-insensitivepoint and the second flux-insensitive point.
 11. The apparatus of claim1, wherein the qubit is an Xmon qubit.
 12. The apparatus of claim 1,wherein the readout resonator operates at about 6.65 GHz.
 13. Theapparatus of claim 12, wherein the first flux-insensitive point is atabout 4.5GHz and the second flux-insensitive point is at about 7.2 GHz.14. A method for operating a qubit, the method comprising: accessing anapparatus comprising: a qubit, wherein the qubit operates over a qubitfrequency spectrum with a first flux-insensitive point and a secondflux-insensitive point; a readout resonator, wherein the readoutresonator operates at a readout resonator frequency in-between the firstflux insensitive point and the second flux-insensitive point; afrequency controller configured to control the frequency of the qubitsuch that during a quantum computation the frequency of the qubit isadjusted relative to the readout resonator frequency; and controllingthe frequency of the qubit such that during a quantum computation thefrequency of the qubit is adjusted relative to the readout resonator.15. The method of claim 14, wherein during the quantum computation thefrequency of the qubit is adjusted relative to the readout resonatorfrequency to perform a downward qubit level transition.
 16. The methodof claim 14, further comprising controlling the frequency of the qubitsuch that during the quantum computation the qubit operates at the firstflux-insensitive point or the second flux-insensitive point.
 17. Themethod of claim 14, wherein the qubit comprises an asymmetricsuperconducting quantum interference device (SQUID), and wherein thelocation of the first flux-insensitive point and the secondflux-insensitive point in the qubit frequency spectrum depends on anasymmetry factor of the SQUID.
 18. The method of claim 17, wherein theratio of the frequency of the first flux-insensitive point to thefrequency of the second flux-insensitive point depends on the asymmetryfactor of the SQUID.
 19. The method of claim 18, wherein the asymmetryfactor of the SQUID is given by${A = \frac{1 + R^{2}}{1 - R^{2}}},{R = \frac{\sqrt{A - 1}}{\sqrt{A + 1}}}$where A represents the asymmetry factor, R represents the ratio of thefrequency of the first flux-insensitive point to the frequency of thesecond flux-insensitive point and A>1, R<1.
 20. The method of claim 14,wherein controlling the frequency of the qubit such that during aquantum computation the frequency of the qubit is adjusted relative tothe readout resonator comprises putting the qubit frequency at or nearthe resonator frequency.
 21. The method of claim 14, wherein controllingthe frequency of the qubit such that during quantum computation thefrequency of the qubit is adjusted relative to the readout resonatorcomprises applying adiabatic swapping to adjust the frequency of thequbit relative to the readout resonator frequency.
 22. The method ofclaim 14, wherein the first flux-insensitive point is lower than thesecond flux-insensitive point, and wherein during the quantumcomputation the qubit operates at the lower flux-insensitive point. 23.The method of claim 14, wherein the readout resonator frequency is atleast a predetermined distance away from both the first flux-insensitivepoint and the second flux-insensitive point.
 24. An apparatus,comprising: a qubit, wherein the qubit operates at a qubit frequencyover a qubit frequency spectrum; a readout resonator, wherein thereadout resonator operates at a readout resonator frequency below thequbit frequency; and a frequency controller configured to control thefrequency of the qubit such that during a quantum computation thefrequency of the qubit is adjusted relative to the readout resonatorfrequency.
 25. The apparatus of claim 1, wherein during the quantumcomputation the frequency of the qubit is adjusted relative to thereadout resonator frequency to perform a downward qubit leveltransition.
 26. The apparatus of claim 24, further comprising a Purcellfilter, wherein the Purcell filter is centered around a Purcell filterfrequency.
 27. The apparatus of claim 26, wherein the Purcell filterfrequency is lower than the qubit operating frequency.
 28. The apparatusof claim 27, wherein the Purcell filter frequency is about 4.5 GHz. 29.The apparatus of claim 24, wherein the qubit frequency spectrumcomprises frequencies between about 4.5 and 6.5 GHz.
 30. The apparatusof claim 24, wherein the readout resonator operates at about 1 GHz belowthe qubit operating frequency.
 31. The apparatus of claim 24, whereinthe qubit comprises a superconducting qubit.
 32. The apparatus of claim24, wherein to adjust the qubit frequency relative to the readoutresonator frequency the frequency controller is configured to set thequbit frequency at or near the resonator frequency.
 33. The apparatus ofclaim 24, wherein during the quantum computation the frequencycontroller is configured to apply adiabatic swapping to adjust thefrequency of the qubit relative to the readout resonator frequency. 34.A method for operating a qubit, the method comprising: accessing anapparatus comprising: a qubit, wherein the qubit operates at a qubitoperating frequency over a qubit frequency spectrum; a readoutresonator, wherein the readout resonator operates at a readout resonatorfrequency below the qubit operating frequency; and a frequencycontroller that controls the frequency of the qubit such that during aquantum computation the frequency of the qubit is adjusted relative tothe readout resonator frequency; and controlling the frequency of thequbit such that during a quantum computation the frequency of the qubitis adjusted relative to the readout resonator.
 35. The method of claim34, wherein during the quantum computation the frequency of the qubit isadjusted relative to the readout resonator frequency to perform adownward qubit level transition.
 36. The method of claim 34, wherein theapparatus further comprises a Purcell filter, wherein the Purcell filteris centered around a Purcell filter frequency.
 37. The method of claim36, wherein the Purcell filter frequency is lower than the qubitoperating frequency.
 38. The method of claim 34, wherein adjusting thequbit frequency relative to the readout resonator frequency comprisessetting the qubit frequency at or near the resonator frequency.
 39. Themethod of claim 34, wherein during the quantum computation the frequencycontroller applies adiabatic swapping to adjust the frequency of thequbit relative to the readout resonator frequency.